Two-dimensional superconformal field theories from Riemann surfaces with boundary

TL;DR

This paper constructs 2D superconformal field theories from 4D N=4 super Yang-Mills compactified on Riemann surfaces with boundary, analyzing boundary conditions that preserve supersymmetry and calculating the resulting central charge.

Contribution

It introduces boundary conditions for twisted compactification that preserve supersymmetry and derives the central charge dependence on the Riemann surface topology.

Findings

Boundary conditions preserving supersymmetry are identified.

An N=(2,2) superconformal field theory is obtained.

The central charge depends on the topology of the Riemann surface.

Abstract

We consider a 2-dimensional conformal field theory (CFT) obtained from twisted compactification of the 4-dimensional N=4 super Yang-Mills theory on a Riemann surface with boundary. We find the boundary conditions to preserve some of the supersymmetry. In particular an N=(2,2) superconformal field theory is obtained from supersymmetry breaking due to the boundary from N=(4,4). In this case we calculate the central charge of the CFT and show its dependence on the topology of the Riemann surface.